Statistical mechanics of liquids and fluids in curved space

Advances in Chemical Physics

Volumn 148, Issue , 2013, Pages 251-310

  Tarjus, Gilles ^a   Sausset, François ^b   Viot, Pascal ^a  

^a SORBONNE UNIVERSITÉ   (France)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84882375786     PISSN: 00652385     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article

References (122)

1. J.-L. Barrat and J.-P. Hansen, Basic Concepts for Simple and Complex Liquids, Cambridge University Press, Cambridge, 2003.
2. M. J. Bowick and A. Travesset, Phys. Rep., 344, 255 (2001).
3. D. R. Nelson, T. Piram, and S. Weinberg, Statistical Mechanics of Membranes and Surfaces, World Scientific, Singapore, 2004.
4. K. W. Kratky, J. Comput. Phys., 37, 205 (1980).
5. J. M. Caillol and D. Levesque, J. Chem. Phys., 94, 597 (1991).
6. J. P. Hansen, D. Levesque, and J. J. Weis, Phys. Rev. Lett., 43, 979 (1979).
7. J.-F. Sadoc and R. Mosseri, Geometrical Frustration, Cambridge University Press, Cambridge, 1999.
8. F. C. Frank, Proc. R. Soc. Lond. A, 215, 43 (1952).
9. D. R. Nelson, Defects and Geometry in Condensed Matter Physics, Cambridge University Press, Cambridge, 2002.
10. M. Kléman and J.-F. Sadoc, J. Phys. Lett., 40, 569 (1979).
11. M. Rubinstein and D. R. Nelson, Phys. Rev. B, 28, 6377 (1983).
12. D. R. Nelson, Phys. Rev. B, 28, 5515 (1983).
13. A. J. Post and E. D. Glandt, J. Chem. Phys., 85, 7349 (1986).
14. B. P. Binks, Curr. Opin. Colloid Interface Sci., 7, 21 (2002).
15. R. Aveyard, B. P. Binks, and J. H. Clint, Adv. Colloid Interface Sci., 100-102, 503 (2003).
16. S. U. J. Pickering, J. Chem. Soc. Trans., 91, 2001 (1907).
17. P. Lipowsky, et al., Nat. Mater., 4, 407 (2005).
18. A. R. Bausch, M. J. Bowick, A. Cacciuto, A. D. Dinsmore, M. F. Hsu, D. R. Nelson, M. G. Nikolaides, A. Travesset, and D. A. Weitz, Science, 299, 1716 (2003).
19. A. B. Subramaniam, M. Abkarian, and H. A. Stone, Nat. Mater., 4, 553 (2005).
20. A. B. Subramaniam, M. Abkarian, L. Mahadevan, and H. A. Stone, Langmuir, 22, 10204 (2006).
21. S. Tarimala, S. R. Ranabothu, J. P. Vernetti, and L. L. Dai, Langmuir, 20, 5171 (2004).
22. J.-F. Sadoc and J. Charvolin, Acta Crystallogr., A45, 10 (1988).
23. J. Meunier,D. Langevin, and N. Boccara, Physics of Amphiphilic Layers, Springer-Verlag, Berlin, 1987.
24. D. A. Hajduk, P. E. Harper, S.M. Gruner, C. C. Honeker, G. Kim, E. L. Thomas, and L. J. Fetters, Macromolecules, 27, 4063 (1994).
25. M. Abkarian, A. B. Subramaniam, S.-H. Kim, R. J. Larsen, S.-M. Yang, and H. A. Stone, Phys. Rev. Lett., 99, 188301 (2007).
26. A. B. Subramaniam, M. Abkarian, L. Mahadevan, and H. A. Stone, Nature, 438, 930 (2005).
27. M. J. Bowick and L. Giomi, Adv. Phys., 58, 449 (2009).
28. T. L. Hill, Thermodynamics of Small Systems, Vols. 1 and 2, Benjamin, New York, 1963.
29. D. Hilbert and S. Cohn-Vossen, Geometry and the Imagination, Chelsea Pub. Co., New York, 1952.
30. H. S. M. Coxeter, Introduction to Geometry, 2nd ed., Wiley, New York, 1969.
31. C. D. Modes and R. D. Kamien, Phys. Rev. E, 77, 041125 (2008).
32. C. D. Modes and R. D. Kamien, Phys. Rev. Lett., 99, 235701 (2007).
33. J. H. P. McKean and I. M. Singer, J. Differential Geom., 1, 43 (1967).
34. F. Sausset and G. Tarjus, J. Phys. A Math. Gen., 40, 12873 (2007).
35. C. Domb, Adv. Phys., 9, 245 (1960).
36. M. Mézard and G. Parisi, Eur. Phys. J. B, 20, 217 (2001).
37. A. Terras, Harmonic Analysis on Symmetric Spaces and Applications, Springer-Verlag, New York, 1985.
38. A. Goetz, Introduction to Differential Geometry, Addison-Wesley, Reading, 1970.
39. J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids, Academic Press, 1986.
40. K. Kratky and W. Schreiner, J. Comput. Phys., 47, 313 (1982).
41. L. A. Fanti and E. D. Glandt, Mol. Simul., 2, 163 (1989).
42. W. Schreiner and K. W. Kratky, Mol. Phys., 50, 435 (1983).
43. J. S. Rowlinson and B. Widom, Molecular Theory of Capillarity, Clarendon, Oxford, 1982.
44. F. Sausset, G. Tarjus, and P. Viot, J. Stat. Mech., P04022 (2009).
45. R. Fantoni, B. Jancovici, and G. Téllez, J. Stat. Phys., 112, 27 (2003).
46. S. Lishchuk, Physica A, 369, 266 (2006).
47. S. Helgason, Indag. Math., 16, 531 (2005).
48. B. J. Gonzalez and E. R. Negrin, Proc. Amer. Math. Soc., 125, 3243 (1997).
49. A. J. Post and E. D. Glandt, J. Chem. Phys., 88, 5805 (1988).
50. A. D. Buckingham and B. D. Utting, Annu. Rev. Phys. Chem., 21, 287 (1970).
51. B. Jancovici and G. Téllez, J. Stat. Phys., 91, 953 (1998).
52. J. M. Caillol, J. Chem. Phys., 96, 1455 (1992).
53. J. M. Caillol and D. Levesque, J. Chem. Phys., 96, 1477 (1992).
54. J. M. Caillol, D. Levesque, J. J. Weis, and J. P. Hansen, J. Stat. Phys., 28, 325 (1982).
55. J. Caillol and D. Gilles, J. Stat. Phys., 100, 905 (2000).
56. J.-M. Caillol, J. Chem. Phys., 99, 8953 (1993).
57. J. P. Straley, Phys. Rev. B, 30, 6592 (1984).
58. J. P. Straley, Phys. Rev. B, 34, 405 (1986).
59. J. Tobochnik and P. M. Chapin, J. Chem. Phys., 88, 5824 (1988).
60. S. Prestipino, M. Ferrario, and P. Giaquinta, Physica A, 187, 456 (1992).
61. S. Prestipino, M. Ferrario, and P. Giaquinta, Physica A, 201, 649 (1993).
62. J. M. Caillol, J. Chem. Phys., 109, 4885 (1998).
63. J. M. Caillol and D. Levesque, Phys. Rev. B, 33, 499 (1986).
64. J. M. Caillol, J. Chem. Phys., 111, 6528 (1999).
65. A. Pérez-Garrido and M. A. Moore, Phys. Rev. B, 58, 9677 (1998).
66. M. W. Roth and M. K. Balasubramanya, Phys. Rev. B, 62, 17043 (2000).
67. M. A. Moore and A. Pérez-Garrido, Phys. Rev. Lett., 82, 4078 (1999).
68. F. Sausset, G. Tarjus, and P. Viot, Phys. Rev. Lett., 101, 155701 (2008).
69. F. Sausset and G. Tarjus, Phys. Rev. Lett., 104, 065701 (2010).
70. F. Sausset, G. Tarjus, and D. R. Nelson, Phys. Rev. E, 81, 031504 (2010).
71. W. Schreiner and K. Kratky, J. Chem. Soc. Trans. 2, 78, 379 (1982).
72. L. T. Wille, J. Phys. A Math. Gen., 20, L1211 (1987).
73. J.-M. Caillol, J. Phys. A Math. Gen., 37, 3077 (2004).
74. C. Monthus and C. Texier, J. Phys. A Math. Gen., 29, 2399 (1996).
75. J. Nissfolk, T. Ekholm, and C. Elvingson, J. Chem. Phys., 119, 6423 (2003).
76. P. Castro-Villarreal, J. Stat. Mech., P08006 (2010).
77. F. Sausset and G. Tarjus, Philos. Mag., 88, 4025 (2008).
78. S. V. Lishchuk, Europhys. Lett., 85, 56001 (2009).
79. M. L. de Haro, A. Santos, and S. B. Yuste, J. Chem. Phys., 129, 116101 (2008).
80. D. R. Nelson and B. I. Halperin, Phys. Rev. B, 19, 2457 (1979).
81. A. P. Young, Phys. Rev. B, 19, 1855 (1979).
82. J. P. Hansen and P. Viot, J. Stat. Phys., 38, 823 (1985).
83. F. Cornu and B. Jancovici, J. Stat. Phys., 49, 33 (1987).
84. G. Orkoulas and A. Z. Panagiotopoulos,J. Chem. Phys., 104, 7205 (1996).
85. P. Choquard, B. Piller, and R. Rentsch, J. Stat. Phys., 46, 599 (1987).
86. P. A. Martin, Rev. Mod. Phys., 60, 1075 (1988).
87. B. Jancovici and G. Téllez, J. Stat. Phys., 116, 205 (2004).
88. M. Baus and J.-P. Hansen, Phys. Rep., 59, 1 (1980).
89. B. Jancovici, Phys. Rev. Lett., 46, 386 (1981).
90. J. Caillol, J. Phys. Lett., 42, 245 (1981).
91. M. Hastings, J. Stat. Phys., 90, 311 (1998).
92. R. Fantoni and G. Tellez, J. Stat. Phys., 133, 449 (2008).
93. C. G. Callan and F. Wilczek, Nucl. Phys. B, 340, 366 (1990).
94. R. Rietman, B. Nienhuis, and J. Oitmaa, J. Phys. A Math. Gen., 25, 6577 (1992).
95. J. C. Angl'es d'Auriac, R. Mélin, P. Chandra, and B. Douçot, J. Phys. A Math. Gen., 34, 675 (2001).
96. B. Doyon, J. Phys. A Math. Gen., 37, 359 (2004).
97. R. R. Singh, K. S. Pitzer, J. J. de Pablo, and J. M. Prausnitz, J. Chem. Phys., 92, 5463 (1990).
98. J. D. Bernal, Nature, 183, 141 (1959).
99. J. P. Sethna, Phys. Rev. B, 31, 6278 (1985).
100. D. Kivelson, S. Kivelson, X. Zhao, Z. Nussinov, and G. Tarjus, Physica A, 219, 27 (1995).
101. G. Tarjus, S. A. Kivelson, Z. Nussinov, and P. Viot, J. Phys. Condens. Matter, 17, R1143 (2005).
102. E. P. Bernard and W. Krauth, arXiv: 1102.4094 (2011).
103. J. C. Maxwell, Philos. Mag., 27, 598 (1864).
104. S. Alexander, Phys. Rep., 296, 65 (1998).
105. M. Wyart, L. E. Silbert, S. R. Nagel, and T. A. Witten, Phys. Rev. E, 72, 051306 (2005).
106. A. J. Liu and S. R. Nagel, Nature, 396, 21 (1998).
107. P. J. Steinhardt, D. R. Nelson, and M. Ronchetti, Phys. Rev. B, 28, 784 (1983).
108. G. Leibon and D. Letscher, Symposium on Computational Geometry (2000) pp. 341-349.
109. D. H. E. Gross, Phys. Rep., 279, 119 (1997).
110. J. J. Thomson, Philos. Mag., 7, 237 (1904).
111. D. Caspar and A. Klug, Cold Spring Harbor. Symp. Quant. Biol., 27, 1 (1962).
112. A. Travesset, Phys. Rev. E, 72, 036110 (2005).
113. M. J. Bowick, D. R. Nelson, and A. Travesset, Phys. Rev. B, 62, 8738 (2000).
114. M. Bowick, H. Shin, and A. Travesset, Phys. Rev. E, 75, 021404 (2007).
115. V. Vitelli, J. B. Lucks, and D. R. Nelson, PNAS, 103, 12323 (2006).
116. D. Nelson and L. Peliti, J. Phys. (France), 48, 1085 (1987).
117. M. Bowick, A. Cacciuto, D. R. Nelson, and A. Travesset, Phys. Rev. Lett., 89, 185502 (2002).
118. R. Backofen, A. Voigt, and T. Witkowski, Phys. Rev. E, 81, 025701 (2010).
119. M. J. W. Dodgson and M. A. Moore, Phys. Rev. B, 55, 3816 (1997).
120. T. Einert, P. Lipowsky, J. Schilling, M. J. Bowick, and A. R. Bausch, Langmuir, 21, 12076 (2005).
121. W. T. M. Irvine, V. Vitelli, and P. M. Chaikin, Nature, 468, 947 (2010).
122. A. M. Turner, V. Vitelli, and D. R. Nelson, Rev. Mod. Phys., 82, 1301 (2010).